#!/usr/bin/env python
# -*- coding: utf-8 -*-
# @Time    : 2020/9/1 15:34
# @USER    : Shengji He
# @File    : PredictWinner.py
# @Software: PyCharm
# @Version  : Python-
# @TASK:
from typing import List


class Solution:
    def PredictTheWinner(self, nums: List[int]) -> bool:
        """
        Given an array of scores that are non-negative integers. Player 1 picks one of the numbers from either 
        end of the array followed by the player 2 and then player 1 and so on. Each time a player picks a number, 
        that number will not be available for the next player. This continues until all the scores have been chosen. 
        The player with the maximum score wins.

        Given an array of scores, predict whether player 1 is the winner. You can assume each player 
        plays to maximize his score.
        
        Example 1:
            Input: [1, 5, 2]
            Output: False
            Explanation: Initially, player 1 can choose between 1 and 2. 
            If he chooses 2 (or 1), then player 2 can choose from 1 (or 2) and 5. If player 2 chooses 5,
            then player 1 will be left with 1 (or 2).
            So, final score of player 1 is 1 + 2 = 3, and player 2 is 5. 
            Hence, player 1 will never be the winner and you need to return False.
         
        
        Example 2:
            Input: [1, 5, 233, 7]
            Output: True
            Explanation: Player 1 first chooses 1. Then player 2 have to choose between 5 and 7.
            No matter which number player 2 choose, player 1 can choose 233.
            Finally, player 1 has more score (234) than player 2 (12), so you need to return True
            representing player1 can win.

        Constraints:
            - 1 <= length of the array <= 20.
            - Any scores in the given array are non-negative integers and will not exceed 10,000,000.
            - If the scores of both players are equal, then player 1 is still the winner.

        :param nums:
        :return:
        """
        # recursion
        # def total(start: int, end: int, turn: int):
        #     if start == end:
        #         return nums[start] * turn
        #     scoreStart = nums[start] * turn + total(start + 1, end, - turn)
        #     scoreEnd = nums[end] * turn + total(start, end - 1, -turn)
        #     return max(scoreStart * turn, scoreEnd * turn) * turn
        # return total(0, len(nums) - 1, 1) >= 0

        # dynamic programming
        length = len(nums)
        dp = [0] * length
        for i, num in enumerate(nums):
            dp[i] = num
        for i in range(length - 2, -1, -1):
            for j in range(i + 1, length):
                dp[j] = max(nums[i] - dp[j], nums[j] - dp[j - 1])
        return dp[length - 1] >= 0


if __name__ == '__main__':
    S = Solution()
    nums = [1, 5, 2]
    print(S.PredictTheWinner(nums))
    print('done')
